Direct Observation of Magnetic Bubble Lattices and Magnetoelastic Effects in van der Waals Cr2Ge2Te6

Ferromagnetic van der Waals (vdW) materials are of large current interest for the fundamental study of low‐dimensional magnetism and for potential applications in multilayer heterostructures. Cr2Ge2Te6 (CGT) is particularly exciting because it is a ferromagnetic semiconductor with tunable electronic and magnetic properties. Controlling the magnetic domain structure of CGT is a requirement for understanding its novel interface physics and for tuning behavior for potential devices. Herein, cryo‐Lorentz transmission electron microscopy is performed in the temperature range of 12–50K to directly image the magnetic domain structures in CGT. A rich phase diagram of domain structures including stripe domains, magnetic bubble lattices of mixed‐chirality, and topologically‐protected lattices of homochiral magnetic bubbles is observed. The types and chiralities of the bubbles can be controlled by topographical changes in the CGT flakes. Additionally, it is observed that in‐plane strain and magnetoelastic coupling can align and organize both bubble lattices and stripe domains. This study provides insights into creating and controlling complex magnetic domain structures for integration into multilayer heterostructures and for future studies of 2D magnetism.


Introduction
The emergence and discovery of long range order in 2D magnetic van der Waals (vdW) materials has opened new areas for research into both fundamental and applied magnetism in reduced dimensions. This includes foundational studies of Moire magnetism and interface physics via integration of the www.afm-journal.de www.advancedsciencenews.com 2214203 (2 of 9) © 2023 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH an interfacial Dzyaloshinskii Moriya interaction (DMI) and can have a relatively high Curie temperature of 220 K. [20,22,23] A particularly interesting magnetic vdW material is Cr 2 Ge 2 Te 6 (CGT). CGT is a semiconductor in which ferromagnetism has been observed down to a bilayer thickness, [8] and it exhibits several spintronic phenomena such as electric-field-or interface-tuned magnetism and giant tunnelling magnetoresistence. [24][25][26][27] Unlike Fe 3 GeTe 2 , CGT does not have a DMI to stabilize topological spin structures, [28] but the domain structures can still affect optical, electrical, and magnonic properties and are therefore an important factor when considering interface induced physics. [27,[29][30][31][32][33] CGT is a semiconductor with a reported band gap of 0.2-0.7 eV, and it can be tuned to show metallic behavior by applying pressure [34] or via ion intercalation. [35] Additionally, CGT displays high magnetostriction, wherein there is a strong magnetoelastic coupling between the magnetization and the crystal lattice, [36,37] and it has shown that T c can be increased with the application of external strain. [18,38] CGT additionally has a negative in-plane thermal expansion coefficient when cooled to and below T c , [36,37] and the induced strains when cooling must be taken into account when considering interfacing CGT with other materials. [18] The complex domain structure, spintronic behavior, and magnetoelastic interactions all make CGT an intriguing material for integration into multilayer heterostructures for the creation of low-power spintronic devices and studies of interface magnetism. [39,40] However, understanding the local effect of strain and magnetoelastic coupling on the domain structure in CGT has largely been unexplored.
In this work, we image the magnetic domain structure of CGT at liquid helium temperatures (<80 K) via in situ cryo-Lorentz transmission electron microscopy (TEM). We can create magnetic bubbles which, while topologically protected as individual spin structures, can form both topologically-trivial lattices of mixed chirality bubbles as well as topologically-protected lattices of homochiral bubbles. These bubble lattices can be easily influenced by additional energy terms, which can arise from topographical variations in the CGT flake as well as through the Villari effect (inverse-magnetostrictive effect) induced by strain. Our work not only shows the presence of topologicallyprotected magnetic bubble lattices in a non-chiral vdW material, but also how to control these lattices. It thus paves the way for interfacing diverse magnetic structures in vdW heterostructures in controlled and reproducible ways.

Results and Discussion
CGT adopts the 3 R space group with layer stacking along the (001) direction and an in-plane rhombohedral packing order as shown in Figure 1a. The in-plane lattice parameters are a = b = 0.6809 nm at 270 K and increase to a = b = 0.6820 nm at 5 K, which arises from in-plane expansion during cooling that is maximal near T c . [36] CGT expands only in-plane during cooling, and the c-axis decreases monotonically with temperature. The van der Waals gap between the layers is clearly visible in the high-resolution transmission electron microscopy (HRTEM) images in Figure 1b,c, recorded along the 〈210〉 and 〈110〉 zone axes respectively. In order to estimate T c and the magnetic anisotropy of our CGT material, we performed magnetometry measurements on a bulk crystal. Magnetization versus temperature curves show a separation when the sample has been zero-field-cooled (ZFC) versus field-cooled (FC) in a 1000 Oe field applied along the c-axis, which indicates the presence of compensating magnetic domains that reduce the total magnetic moment. The Curie temperature can be calculated by extrapolating the slope of the FC curve from its point of inflection and finding its intercept on the x-axis, giving a value of T c = 64.5 K. Figure 1e shows a plot of hysteresis loops measured along the c-axis of the CGT, as a function of temperature, showing that the saturation magnetization increases with reduced temperature down to 20 K. By comparing the in-plane hysteresis loop and the out-of-plane loop, we calculated the first uniaxial anisotropy constant to be K u1 = 3.79 × 10 4 J m −3 at 10 K, which fits well with previous measurements. [41] To characterize the electronic behavior of CGT, we measured the resistivity as a function of temperature. Figure 1f shows an exponentially drop in the resistivity when the temperature is below T c . By fitting with an Arrhenius equation R = R 0 exp (E g /2k B T), we determine the band gap to be 0.14 eV, consistent with other values derived from transport measurements. [26,36,42] . This finding suggests that the CGT crystal that we are measuring is semiconducting at ambient pressure.
CGT flakes were exfoliated from bulk crystals and directly transferred using a dry process onto a 50 nm thick SiN membrane window for TEM imaging. This resulted in both large flat regions of flake in which domains could be imaged over large fields of view, and also flake regions with step boundaries, wrinkles, and other large-scale defects that were observed to impact the magnetic domain structure.
We performed cryogenic Lorentz transmission electron microscopy (LTEM) imaging using a liquid helium holder with which we could reach temperatures as low as 12 K. Although we measured T c of our bulk CGT crystal to be 72.0 K, the onset temperature for magnetic domains is significantly reduced in thinner flakes, with values ranging from 50 to 64 K in flakes ranging in thickness from 55 to 175 nm. Here we consider T c to be the point at which magnetic domains becomes visible during cooling. When in LTEM mode, the objective lens can be excited to apply a magnetic field to the sample along the electron beam direction. This allowed us to perform in situ fieldcooling experiments with applied field strengths ranging from 1370 to 155 Oe, which was the minimum remnant field when the objective lens was turned off.
We observed a range of magnetic domain structures including stripe domains and bubble lattices, with all of the domain walls and magnetic bubbles being of Bloch type. Figure 2a shows a LTEM image of CGT imaged along the c-axis, taken at 20 K with a −800 µm defocus, after the sample was field-cooled in a 155 Oe out-of-plane field. For all samples, the field-cooling process involved applying the specified field at a temperature above T c and maintaining that field when cooling (and while taking images unless otherwise noted). After fieldcooling in a 155 Oe field, we observe primarily maze domains with some bubbles. After field-cooling in a larger applied field, we observe magnetic bubbles across large regions of the sample as shown in Figure 2b,c. The shape and size of the bubbles are more uniform when cooling in a 500 Oe field as opposed to 300 Oe. When field-cooling with stronger applied fields, maze domains are once again formed until the saturation field is reached. This observation of a region of stability for magnetic bubbles, with weaker or stronger fields leading to the formation of maze domains, is identical to the behavior observed in other materials that exhibit skyrmions. [43] However, in CGT there is no DMI to define bubbles of a uniform chirality, and thus both right-and left-handed bubbles can be stabilized by the balance of Zeeman, dipolar, and other material-dependent energy terms. In the case of lattices containing bubbles with both chiralities, that is, "mixed-chirality bubble lattices", while each of these bubbles on their own is a topologically-protected Figure 2. Magnetic domain structure of CGT at 20K under various field conditions. a-d) LTEM images of domains after field-cooling in out-of-plane fields from 155 to 800 Oe. Maze domains are seen at high and low field strengths, and magnetic bubbles are formed for applied fields ranging from 300 to 700 Oe. e-g) The sample shown in (c), which was field-cooled in a 500 Oe applied field, is subjected to an increasing field and the bubbles shrink and are driven out of the sample. h) When the field is reduced to 155 Oe, the domains expand and form a mixture of mazes and bubbles. quasiparticle, the lattice as a whole will have a neutral topological charge. Despite this, the mixed-chirality bubble lattices that we observe behave similarly to skyrmion lattices upon increasing the applied field. Figure 2e through Figure 2h shows the effect of applying an increasing field at 20 K to the 500 Oe field-cooled sample shown in Figure 2c. The bubbles initially contract until a field at which some bubbles are driven out of the sample, with no apparent preference for chirality as shown by the equal proportion of bubbles with bright and dark centers. We did not observe any indication of opposite chirality bubbles merging or annihilating. Upon returning to the remnant field of 155 Oe, the bubbles that remain expand in size with some elongating and deforming to fill the space and reduce the dipole energy.
We observed two types of magnetic bubbles in CGT that can be characterized by their chirality and topology. The majority of the bubbles we observed, including those depicted in Figure 2, are Type I vortex-state bubbles. We also observed the less common Type II "onion"-state bubbles. [44] Type I bubbles are topologically protected with either a right-or left-handed chirality, while Type II bubbles contain internal domain walls, across which the circulation reverses, and are topologically trivial. [45] The magnetization configurations of these bubble types are shown in Figure 3a-c.
When electrons pass through a ferromagnetic sample, the magnetic vector potential induces a phase shift according to the Aharonov-Bohm equation. [46] For Type I Bloch bubbles, this leads to a uniform phase shift that is positive or negative depending on bubble chirality. For Type II bubbles, a less intense, alternating phase shift is observed, as shown in Figure 3d-f. Reconstructed LTEM phase images are therefore a useful method for clearly showing the chirality distribution of bubbles across an image. Figure 3g-i shows the resulting LTEM images corresponding to these phase shifts, for a defocus value of Δz = − 800 µm. The simulated images of Type I bubbles match well to the experimental data shown in Figure 2. A through-focus-series of LTEM images can be used to reconstruct the phase shift and in-plane magnetic induction maps via the transport of intensity equation (TIE) method. [47,48] The integrated induction maps are shown in Figure 3j-l and for Bloch bubbles appear qualitatively similar to the true inplane magnetization. Figure 3m-r shows experimental LTEM images and integrated induction maps corresponding to the three simulated magnetization patterns. For all cases, both the LTEM image and the induction map are reproduced well by the simulations.
Some magnetic systems that lack a DMI have been shown to support magnetic bubbles of mixed chirality such as those shown seen in Figure 2c. [49] These materials did not display any homochiral bubble lattices. In other systems, however, lattices of homochiral magnetic bubbles have been observed where all bubbles have the same chirality. [28,50] The chirality of the lattice is not intrinsic to the material and is therefore random, with a 50% chance of forming with either chirality every time the bubble lattice is formed after magnetic saturation or heating above T c . Although these materials lack a DMI, the magnetic bubbles were always found to be homochiral across the lattice. Surprisingly, in CGT we observe both homochiral bubble lattices that are functionally identical to skyrmions, as well as mixed-chirality lattices containing both right-and left-handed bubbles in equal proportions.  of a CGT sample after twice field-cooling it to 22 K in a 500 Oe applied field. In Figure 4a, the uniform positive phase shift across all of the bubbles indicates a homochiral lattice of righthanded chirality bubbles. After warming the sample above T c and performing the same field-cooling procedure, we observed a mixed-chirality bubble lattice in the same region, as shown in Figure 4b,d. Apart from the difference in chirality distribution, the two bubble lattices are very similar, with the size and distribution of the bubbles being independent of the global lattice topology. The primary difference between the two lattices was the rare presence of topologically-trivial Type II bubbles that formed solely in mixed-chirality bubble lattices. These bubbles can be identified by their alternating black/white phase contrast as shown in Figure 3f.
We consistently observed the formation of both mixedchirality and homochiral bubble lattices across multiple CGT samples. We found that whether a homochiral or mixed-chirality bubble lattice forms is a stochastic process: within any one region of a flake, repeated identical field-cooling runs could give rise to either a mixed-chirality or a homochiral lattice, which indicates that the effect is not due to microstructural or compositional variations in our samples. We were furthermore unable to enforce the creation of either type of lattice by controlling the applied field strength or the cooling rate. We did observe both mixed-chirality and homochiral bubble lattices in the same flake after a single field-cooling process, but in almost all cases the lattices were separated by large scale disruptions such as wrinkles. In one experiment we observed a homochiral bubble lattice and a mixed-chirality lattice separated only by an extended defect in the sample, but this was not found to be repeatable (see Section S1, Supporting Information). Observations of the same region after subsequent field-cooling runs led to either homochiral or mixed-chirality bubble lattices that extended across the defect.
Although flat regions of CGT sometimes contained homochiral bubble lattices, flake regions with topographical variations consistently showed mixed-chirality lattices, leading to a potential method for affecting the net topology of the magnetic domain structure in CGT. Figure 4e shows a phase image of a region of a CGT flake that contains both homochiral and mixed-chirality lattices of magnetic bubbles. Some wrinkles and folds in the flake can form during the exfoliation process, and the image shown in Figure 4e is of a region close to such a wrinkle. The region to the right of the image is flat, but the left side approaches a fold in the flake, such that it is slightly bent or lifted away from the SiN window without a measurable change in thickness. The flat region contains predominantly homochiral bubbles, and an integrated induction map from this region is shown in Figure 4g. Closer to the wrinkle on the left side of the image, we observe bubbles of both chiralities, similar to what is shown in Figure 4b. However, unlike mixed-chirality bubble lattices in flat regions of the flake, here we also observe deformed bubbles that are elongated into stripe domains (see Section S2, Supporting Information), as well as a higher concentration of topologically-trivial Type II bubbles as shown in Figure 4f. One of the Type II bubbles from this region is also shown in Figure 3o,r, where both the LTEM image and TIE reconstruction match well to simulation.
We have shown how variations in the topography of the flake can disrupt a bubble lattice of otherwise uniform chirality, but the magnetization can also be influenced directly by magnetoelastic coupling to the crystal structure. It has previously been deduced from Raman measurements that large hydrostatic pressures can alter the strength of exchange interactions in CGT, [38] and also that CGT can display a pressure-induced spin reorientation in which the easy axis of the magnetization switches from aligning along the c-axis to an in-plane easy plane. [51] We have directly observed stress-induced changes in the domain structure of CGT due to an in-plane strain that is caused by the material expanding during field-cooling. Due to the increase in the lattice parameters a and b when cooling through T c , the CGT flake we image at low temperatures has a larger in-plane area than at room temperature. This means that there is a compressive in-plane strain. When exfoliating the CGT flake onto the SiN membrane, some regions of the flake are firmly fixed to the membrane while other regions are not. The unattached parts can then buckle or wrinkle under this compressive strain. [18] When imaging using TEM, buckled regions create regular and repeating bend contour contrast that we observe perpendicular to the a-axis. We find that the magnetization responds differently when varying temperature and applied field in these buckled regions, and this allows us to directly observe magnetoelastic effects on the domain structure in CGT without requiring an external application of strain. Figure 5 shows how magnetoelastic coupling can align bubble lattices and stripe domains in regions with strain. The sample was first field-cooled in a 600 Oe out-of-plane field to 12 K in order to nucleate magnetic bubbles. The field was then reduced to the remnant value of 155 Oe. In Figure 5a the magnetic bubbles, highlighted with orange circles (see Section S3, Supporting Information), show a general alignment along the strained a-axis across the full field of view. The inset shows a fast Fourier transform (FFT) of the bubble locations, which highlights the six-fold symmetry in the bubble lattice. Upon increasing the field strength (Figure 5b through Figure 5d), we see in both the real-space image and the FFT that the lattice order is gradually lost. Individual bubbles are driven out of the sample above 600 Oe, and this leads to uneven packing of the bubbles. The sample is fully saturated in a 1300 Oe field and, when the field is then reduced to 155 Oe, we observe maze domains with Bloch type domain walls that do not display any orientational preference, as shown in Figure 5f.
Figure 5a-f shows that the magnetic domain ordering, that occurs during field cooling, is lost and does not return after exposing the sample to a saturating magnetic field. The order can be restored, however, by heating the sample back to T c . Figure 5g shows a sample in the same state as in 5f, at 12 K with maze domains that were created by saturating the sample in a field of 1300 Oe and then reducing the field to 155 Oe. The corresponding TIE-reconstructed magnetic induction map is shown in Figure 5m, which highlights the branched and curved domain structure. Figure 5h-l shows the effect of increasing the temperature while maintaining the 155 Oe out-of-plane field. Between 12 and 41 K there is little change in the domain structure. With continued heating, the domains become narrower and align along the a-axis before disappearing at T c .
The behavior shown in Figure 5 can be explained by looking at the magnetostrictive properties of CGT as a function of temperature. The magnetostriction coefficient,  Insets show a FFT from the magnetic bubble lattice. The bubbles (some overlaid with orange as a visual aid) remain aligned until some bubbles are driven out of the sample before it is saturated (e). The maze domains that occur after reducing the field (f) show no preferred orientation. g-l) Disorganized maze domains realign as they are heated to T c . m-q) Integrated magnetic induction maps of the region inside the highlighted box shown in (g), for images (g) through (k).
applied along an in-plane direction therefore corresponds to a reduction of the uniaxial anisotropy constant and a preferred alignment of the magnetization along the strain direction. [52] In order to confirm the magnetoelastic properties of our sample, we performed temperature-dependent Raman measurements of a CGT flake exfoliated from the same single crystal as was used for LTEM imaging. In agreement with the literature, we observe a sharp change in phonon frequency due to a change in lattice parameter that occurs at T c [53] . This change can be directly attributed to magnetoelastic coupling at the paramagnetic to ferromagnetic phase transition (see Section S4, Supporting Information). This corresponds to λ a as a function of temperature being sharply peaked near T c , and the magnetization is therefore most susceptible to a change in stress near T c . [52] Below ≈40 K, the magnetostrictive properties of CGT are greatly reduced and strain due to lattice parameter change has a minimal effect on the magnetization.
These magnetoelastic effects that are relevant near T c , namely the reduction of effective anisotropy and preferred alignment of the magnetization parallel to the strain vector, help explain our observations shown in Figure 5. When field-cooling through T c , in the strained regions the lower effective anisotropy reduces the effects of pinning and allows the bubbles to reduce the total energy by forming a more ordered triangular lattice. [54] At 12 K the bubbles are largely pinned, and therefore the sixfold symmetry of the lattice is reduced when individual bubbles are destroyed by the increasing applied field, as shown in Figure 5c,d. The increased pinning and decreased bubble mobility prevent the bubbles from rearranging to restore lattice order at temperatures far below T c .
Additionally, as the magnetoelastic coupling in CGT is very weak below 40 K and the magnetization is less affected by applied stress, the newly formed domains shown in Figure 5f do not align to any preferred orientation. When the sample is heated back to T c , however, the decreasing uniaxial anisotropy and sharply increasing magnetostriction coefficient allow for the creation of more domain walls aligned parallel to the aaxis, as shown in Figure 5g-q. This is seen to occur only once the temperature is above ≈40 K, at which point magnetoelastic effects are relevant and can affect the magnetization.
We have made direct observations of the magnetoelastic coupling between magnetization and strain in CGT. In conjunction with previous works that have shown the bulk effects of strain on the magnetic structure of CGT, [18,38,51,53] this work reveals how the magnetic domain structures are directly affected in measurable ways at the nanoscale. These domain effects should be taken into account when considering any future device applications that involves interfacing CGT with other materials, as the interface quality and degree of strain will heavily influence the magnetic properties of the device. This work further provides a potential method for using strain induced by layered heterostructures and temperature changes to control and create organized magnetic domain structures. This could simplify the interpretation of transport or other non-local measurements in CGT heterostructures.

Conclusion
We have used cryo-LTEM to perform in situ imaging of magnetic domains in CGT. We have observed magnetic bubble lattices containing both uniform-and mixed-chirality bubbles which behave similarly to skyrmions when varying the applied field strength and temperature. Magnetoelastic coupling was shown to align domain structures along the crystalline a-axis when the in-plane magnetostriction coefficient is strongest and the sample is close to T c . Ordered domain structures can therefore be created both directly by field-cooling, and also by heating disordered domain structures back to near T c . We have shown that it is possible to organize and control magnetic bubble lattices in non-chiral materials that lack a DMI.

Experimental Section
Sample Preparation: Crystalline flakes (>1 mm 2 ) of CGT were synthesized in a tellurium flux, using a Cr:Ge:Te ratio of 2:2:35. The starting materials of Chromium powder (99.5%, Aldrich), germanium pieces (99.999%, Plasma Materials), and tellurium pieces (99.99%, American Elements) were charged into a fused silica tube. The tube was evacuated to a pressure of 3.2 × 10 −3 bar and sealed. The tube was inserted into a computer-controlled tube furnace, heated to 700 °C over 12 h, soaked over 100 h, cooled to 400 °C over 80 h. The furnace was then turned off and allowed to naturally cool to room temperature.
After the initial heating, the ingot was loaded into a new fused silica tube and evacuated to a pressure of 3.2 × 10 −3 bar and sealed. For the second heating step, the tubes were placed in a mullite tube with the ingot-containing end adjacent to the thermocouple in the furnace and the other end stuck out of the furnace, exposed to air. Insulation was placed only to the edge of the tube furnace. The tubes were then heated to 500 °C over 6 h and soaked over 24 h. The furnace was then turned off and allowed to cool naturally to room temperature. This distillation of tellurium was repeated 3 times, until all the excess tellurium was visibly removed. TEM samples were prepared by dry exfoliation of single crystals using the tape method, before picking up flakes with a polydimethylsiloxane (PDMS) stamp and transferring them to silicon nitride TEM membrane. The thickness of CGT flakes were measured using atomic force microscopy and ranged from 60 to 150 nm thick. Magnetometry measurments were made on bulk crystal pieces using a SQUID MPMS magnetometer.
LTEM Imaging: Cryo-LTEM imaging was performed on a JEOL JEM-2100F TEM instrument using a Gatan double-tilt liquid helium holder. Imaging was performed in Lorentz mode, which has a residual magnetic field of 155 Oe. The magnetic field along the beam direction was increased by exciting the objective lens, allowing us to maintain the sample in fields ranging from 155 to 1370 Oe. The total electron phase shift through the material was reconstructed using the transport of intensity (TIE) method and the PyLorentz software. [47,48] PyLorentz was also used for simulating electron phase shifts and LTEM images from micromagnetics simulated magnetizations.
Raman Measurements: CGT flakes were exfoliated onto a Si substrate and immediately loaded into a JANIS cryostat and protected by vacuum (<5× 10 −6 mbar) to avoid degradation. Raman spectra of the flake were collected with an optical microscope in the back-scattering configuration. The beam of a solid-state 561 nm continuous wave laser (Coherent OBIS 561) was focused by a microscope objective (50x, NA = 0.55) to excite the samples. Scattered photons from the sample were collected and measured through a spectrometer (Princeton Instruments SpectraPro HRs-750). The temperature of the sample was controlled and monitored through a Lakeshore Model 335 temperature controller.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.